Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| isoclinism | isoclinic class of #72209606 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C22 | #11757163 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C2×2−1+4 | A5 |
| LCS | G | |
| UCS | C1 ◁ C22 | |
162 conjugacy classes of subgroups; only the 8 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 8 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(2,5)(4,15)(7,21)(8,26)(9,20)(10,23)(11,13)(12,29)(16,24)(17,27)(18,31)(19,32)(22,30)(25,28)(33,34,37,35)(36,39,38,40)(41,45,43,46)(42,47,44,48)(49,51,50,52)(53,56,55,54);(2,3,4)(7,12,16)(8,11,17)(9,13,18)(10,14,19)(20,21,22)(25,30,29)(27,28,31)(33,36,34)(35,37,38)(39,41,42)(40,43,44)(45,48,49)(46,47,50)(51,53,54)(52,55,56);(33,37)(34,35)(36,38)(39,40)(41,43)(42,44)(45,46)(47,48)(49,50)(51,52)(53,55)(54,56);(1,2)(3,11)(4,16)(5,20)(6,10)(7,14)(8,19)(9,23)(12,24)(13,25)(15,31)(17,26)(18,27)(21,28)(22,29)(30,32);(1,3)(2,7)(4,17)(5,21)(6,14)(8,26)(9,28)(10,11)(12,19)(13,23)(15,27)(16,24)(18,30)(20,25)(22,31)(29,32);(1,4)(2,8)(3,12)(5,22)(6,19)(7,24)(9,29)(10,16)(11,26)(13,31)(14,17)(15,28)(18,23)(20,27)(21,30)(25,32);(1,5)(2,9)(3,13)(4,18)(6,23)(7,25)(8,27)(10,20)(11,28)(12,30)(14,21)(15,24)(16,29)(17,31)(19,22)(26,32);(1,6)(2,10)(3,14)(4,19)(5,23)(7,11)(8,16)(9,20)(12,17)(13,21)(15,32)(18,22)(24,26)(25,28)(27,29)(30,31)31 conjugacy classes — view the full character table.
| derived subgroup of | #72227889 |
| maximal subgroup of | #72227889, #72267530, #72267591, … |
| maximal normal subgroup of | #72227889 |
| maximal quotient of | #72238105, #72267635, #72267744, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((2,5)(4,15)(7,21)(8,26)(9,20)(10,23)(11,13)(12,29)(16,24)(17,27)(18,31)(19,32)(22,30)(25,28)(33,34,37,35)(36,39,38,40)(41,45,43,46)(42,47,44,48)(49,51,50,52)(53,56,55,54), (2,3,4)(7,12,16)(8,11,17)(9,13,18)(10,14,19)(20,21,22)(25,30,29)(27,28,31)(33,36,34)(35,37,38)(39,41,42)(40,43,44)(45,48,49)(46,47,50)(51,53,54)(52,55,56), (33,37)(34,35)(36,38)(39,40)(41,43)(42,44)(45,46)(47,48)(49,50)(51,52)(53,55)(54,56), (1,2)(3,11)(4,16)(5,20)(6,10)(7,14)(8,19)(9,23)(12,24)(13,25)(15,31)(17,26)(18,27)(21,28)(22,29)(30,32), (1,3)(2,7)(4,17)(5,21)(6,14)(8,26)(9,28)(10,11)(12,19)(13,23)(15,27)(16,24)(18,30)(20,25)(22,31)(29,32), (1,4)(2,8)(3,12)(5,22)(6,19)(7,24)(9,29)(10,16)(11,26)(13,31)(14,17)(15,28)(18,23)(20,27)(21,30)(25,32), (1,5)(2,9)(3,13)(4,18)(6,23)(7,25)(8,27)(10,20)(11,28)(12,30)(14,21)(15,24)(16,29)(17,31)(19,22)(26,32), (1,6)(2,10)(3,14)(4,19)(5,23)(7,11)(8,16)(9,20)(12,17)(13,21)(15,32)(18,22)(24,26)(25,28)(27,29)(30,31));